This invention is concerned with the use of neural networks to determine optimal control parameters for linear quadratic discrete-time processes.
Optimal control problems are among the most difficult of optimization problems. This class of control problems typically includes equality constraints which are defined in terms of differential/difference equations and various boundary conditions, as well as inequality constraints which involve boundary conditions, entire trajectories, and controls. The implementation of an optimal control strategy for a linear quadratic problem has traditionally required a solution of the Riccati equation. The discrete-time Riccati equation has generally been solved by numerical computation, a recursive method, or an eigenvalue-eigenvector method (See, e.g., Kwakernaak, et al., Linear Optimal Control Systems, Pages 193-327 (Wiley-Interscience 1972)). None of these procedures, however, is straightforward. The recursive method, for example, starts with a boundary condition and solves the Riccati equation backwards. Consequently, in the prior art it has typically been necessary to obtain the solution for an optimal control problem off-line and store the solution in memory. In this approach, the stored information must then be recalled to implement the optimal control on-line. This procedure has the drawback of not being able to deal with the control of a time-varying system.
Because of this and similar limitations of the prior art techniques, it would be desirable to provide a technique which is fast enough to provide optimization of linear quadratic discrete-time controls in real-time.